The straight line through P(x1, y1) inclined at an angle θ with the x–axis meets the line ax + by + c = 0 in Q. Find the length of PQ.
Given: the equation of the line that passes through P(x1, y1) and makes an angle of θ with the x–axis.
To find:
Length of PQ.
Explanation:
Let PQ = r
Then, the coordinates of Q are given by
Formula Used:
⇒
Thus, the coordinates of Q are
Clearly, Q lies on the line ax + by + c = 0.
∴
⇒ r
∴ PQ
Thus, length PQ